Band structures in Sierpinski triangle fractal porous phononic crystals

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• 作者：Kai Wang ; Ying Liu ; ^{yliu5@bjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Tianshu Liang
• 关键词：A. Sierpinski triangle fractal ; B. Porous phononic crystal ; C. Band structure ; D. FEM
• 刊名：Physica B: Physics of Condensed Matter
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：498
• 期：Complete
• 页码：33-42
• 全文大小：3859 K

文摘

In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.